The primary purpose of conducting Tukey pairwise comparisons after a significant ANOVA is to:

In a manufacturing study two machine settings yield average defect rates 14 and 11 (units: percent). Each setting used n = 16 samples, and MSE from ANOVA is 4.0. If the q critical value is 4.30, compute q for these two settings and the Tukey decision.

In a pilot study with groups P, Q, R, S each with n = 6, the ANOVA indicates a significant overall F. MSE = 5.0, group means are P = 10, Q = 12, R = 16, S = 23. Degrees of freedom for error is 24, and the studentized range critical value for k = 4 and df = 24 at alpha = 0.05 is q_crit = 4.03. Calculate which pairwise comparisons are significant.

Which statement best describes the difference between a one-way ANOVA and a two-way ANOVA?

Suppose you are conducting a two-way ANOVA on a dataset with three treatments and four blocks. If the last observation in the third treatment and the second block is altered to be an extreme outlier, what is the most likely effect on the results of the two-way ANOVA?

A two-way ANOVA yields p_interaction = 0.012, p_factorA = 0.004, p_factorB = 0.020 at α = 0.05. Which interpretation is the most appropriate?